Patrick Vieira's side will take on Everton at Selhurst Park, with the tie set to be played over the weekend of March 19-20th.
The Eagles last faced Everton in this season's Premier League, running out 3-1 winners, and were drawn from the velvet hat by Palace Academy graduate and England manager Gareth Southgate.
Everton currently sit 17th in the league, with Frank Lampard joining as manager at the end of January.
They beat Boreham Wood 2-0 to confirm their place in the quarter-final, which Palace last reached in 2018/19.